Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-3x-6y &= 9 \\ -2x-7y &= 7\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-2x = 7y+7$ Divide both sides by $-2$ to isolate $x$ $x = {-\dfrac{7}{2}y - \dfrac{7}{2}}$ Substitute this expression for $x$ in the first equation. $-3({-\dfrac{7}{2}y - \dfrac{7}{2}}) - 6y = 9$ $\dfrac{21}{2}y + \dfrac{21}{2} - 6y = 9$ Simplify by combining terms, then solve for $y$ $\dfrac{9}{2}y + \dfrac{21}{2} = 9$ $\dfrac{9}{2}y = -\dfrac{3}{2}$ $y = -\dfrac{1}{3}$ Substitute $-\dfrac{1}{3}$ for $y$ in the top equation. $-3x-6( -\dfrac{1}{3}) = 9$ $-3x+2 = 9$ $-3x = 7$ $x = -\dfrac{7}{3}$ The solution is $\enspace x = -\dfrac{7}{3}, \enspace y = -\dfrac{1}{3}$.